Microscopic study of low-lying spectra ofΛhypernuclei based on a beyond-mean-field approach with a covariant energy density functional

Abstract

We present a detailed formalism of the microscopic particle-rotor model for hypernuclear low-lying states based on a covariant density functional theory. In this method, the hypernuclear states are constructed by coupling a hyperon to low-lying states of the core nucleus, which are described by the generator coordinate method (GCM) with the particle number and angular momentum projections. We apply this method to study in detail the low-lying spectrum of 13 Λ C and 21 Λ Ne hypernuclei. We also briefly discuss the structure of 155 Λ Sm as an example of heavy deformed hypernuclei. It is shown that the low-lying excitation spectrum with positive parity states of the hypernuclei, which are dominated by Λ hyperon in s-orbital coupled to the core states, are similar to that for the corresponding core states, while the electric quadrupole transition strength, B(E2), from the 2 + 1 state to the ground state is reduced according to the mass number of the hypernuclei. Our study indicates that the energy splitting between the first 1/2 − and 3/2 − hypernuclear states is generally small for all the hypernuclei which we study. However, their configurations depend much on the properties of a core nucleus, in particular on the sign of deformation parameter. That is, the first 1/2 − and 3/2 − states in 13 Λ C are dominated by a single configuration with Λ particle in the p-wave orbits and thus providing good candidates for a study of the Λ spin-orbit splitting. On the other hand, those states in the other hypernuclei exhibit a large configuration mixing and thus their energy difference cannot be interpreted as the spin-orbit splitting for the p-orbits.

Impurity Effects in Λ Hypernuclei

“…In this paper, we compare the parity-projected core states (Ψ π N ) and the corresponding states with a Λ particle in an s orbit (Ψ π N ⊗ Λ) in the hypernuclei. Figure 1(d)-(f) shows the energy curves of 13 Λ C, 21 Λ Ne, and 12 Λ Be, while those of the core nuclei ( 12 C, 20 Ne, and 11 Be) are illustrated in Figure 1(a)-(c). The energies and deformations (β, γ) at the minima are summarized in Table I.…”

“…The core nucleus 20 Ne is a typical sdshell nucleus with various structures within the small excitation energy range [3][4][5]. It is known that the K π = 0 − band has a pronounced α+ 16 O clustering, while the ground-state band shows mixture of deformed shell structure and α + 16 O cluster structure.…”

“…In 13 Λ C and 12 Λ Be, the α cluster structure is enhanced at large β on the energy curves, which makes the overlap I smaller. In 21 Λ Ne, the core nucleus 20 Ne is clusterized into α+ 16 O with a large β. Since 16 O has larger mass number than the α, the decrease of I is suppressed in the α+ 16 O cluster states.…”

“…Since most nuclei manifest quadrupole deformation, it is of interest to investigate changes of nuclear deformations due to the addition of a Λ particle, which many authors have studied [7,[14][15][16][17][18][19][20].…”

“…Furthermore, in 21 Λ Ne, we also discuss the dependence of impurity effects on structures, namely their difference between mean-filed like and α + 16 O + Λ cluster states. In 20 Ne [3][4][5], it is known that the K π = 0 − band has a pronounced α+ 16 O clustering, while the ground-state band has a mixture of deformed shell structure and α + 16 O cluster structure. Another aim is a rather challenging: to show the possibility of using a Λ particle as a probe to investigate structure of the core nuclei.…”